The correct option will be: C. [tex]\frac{19}{9}[/tex]
Explanation
The repeating decimal given is: [tex]2\bar{.1}[/tex] which means 2.1111111111..........
Suppose, the given number 2.1111111111.......... as [tex]x[/tex]
Here the repeating digit is 1 . First, we need to move the decimal point after the repeating digit. So we can do that by multiplying both sides by 10. Thus....
[tex]x= 2.1111111111.........\\ \\ 10x= 21.1111111111.........[/tex]
Now subtracting the above two equations , we will get.....
[tex]10x-x= (21.1111111111.........)-(2.1111111111.........)\\ \\ 9x= 19\\ \\ x= \frac{19}{9}[/tex]
So, the given repeating decimal be expressed in a fraction as [tex]\frac{19}{9}[/tex]
